On C*-algebras associated to right LCM semigroups

Authors

Nathan D. Brownlowe, University of WollongongFollow
Nadia S. Larsen, University of Copenhagen, University of Oslo
Nicolai Stammeier, University of Oslo

RIS ID

110325

Publication Details

Brownlowe, N., Larsen, N. S. & Stammeier, N. (2017). On C*-algebras associated to right LCM semigroups. Transactions of the American Mathematical Society, 369 (1), 31-68.

Abstract

We initiate the study of the internal structure of C*-algebras associated to a left cancellative semigroup in which any two principal right ideals are either disjoint or intersect in another principal right ideal; these are variously called right LCM semigroups or semigroups that satisfy Clifford's condition. Our main findings are results about uniqueness of the full semigroup C*-algebra. We build our analysis upon a rich interaction between the group of units of the semigroup and the family of constructible right ideals. As an application we identify algebraic conditions on S under which C*(S) is purely infinite and simple.